Due to length, this reply is broken into three comments. This is the first comment, the next two are nested under this one

Part 1: The "why"

The 1950s are the first decade with a true visual popular culture. For the first time many families across nearly all income levels could afford a TV. This meant that everybody could see the same programming, together, simultaneously for the first time. Even if you were watching through a store window you were still a participant in this new shared visual culture.

Radios were in nearly every household during WWII and connected people, but television created a cohesive visual identity of America. That the shared identity was idealized or purely fantasy made it easier for people to accept since it was their ideal and their fantasy.

The "all-American housewife and Pipe-smoking Breadwinner Working Father" is associated with 1950s television because entertainment media reflects to us the version of us we want to see. Television does not show us as we are, it shows us as we want to be and how we want to see ourselves. This television portrayal worked because people wanted it to.

Producers and directors were not trying to cement new gender roles, they showed people what they wanted from their own family. The goal for many families was that dad could be the sole earner and mom would not have to work. Through it's characters and ability to be uses as an escape from the "real world" TV made that reality possible for everyone

It is no different than how Friends showed us a group of close friends who have been close for many years including a pair of siblings. Audiences saw them living implausibly well in unrealistically affordable NYC apartments and spending their days not at work, but in a coffee shop. America, and the world thought, "I wish I had that" and "other than the style of living and never going to work that's me and my friends." The show gave us a positive vision of ourselves.

Cheers brought America into a community that we all wanted to be a part of. Who doesn't want to walk into somewhere "everybody knows your name?" Cheers was the perfect third place for Cliff and Norm and a work family for Sam and the rest of the bar's staff.

Somewhat pedantic note, but possibly important: Ira Levin's The Stepford Wives is really much more anchored in the late 60s/early 70s post-sexual-revolution society.

In the 1972 book moreso than the 1975 movie , the "wives" were constructed (literally) to be sexually available, and the descriptions are meant to evoke the semi-legendary swinger/"car-key parties". (There's a bit in the DVD extras which describes the film's iconic sun hats-and-flowing sleeves look as being a result of the director's wife, Nanette Newman, being cast as the main Stepford Wife and not wanting to be too sexy onscreen, despite screenwriter William Goldman's objections.)

Levin's the same novelist who gave us Rosemary's Baby, another popular horror novel based on feminist or "women's lib" issues of the time - a best-seller in 1967 that, in 1968, became an Oscar-winning film.

This might be relevant to your question by way of contrast... the 1950s are the last "before" for which Levin's work is decidedly an "after." The sexual revolution of the 1960s is what fell in between. Someone with more sociological chops can discuss that at greater length.